A Set of Sequences of Complexity
arXiv:1707.02741 · doi:10.1007/978-3-319-66396-8_14
Abstract
We prove the existence of a ternary sequence of factor complexity for any given vector of rationally independent letter frequencies. Such sequences are constructed from an infinite product of two substitutions according to a particular Multidimensional Continued Fraction algorithm. We show that this algorithm is conjugate to a well-known one, the Selmer algorithm. Experimentations (Baldwin, 1992) suggest that their second Lyapunov exponent is negative which presages finite balance properties.
12 pages, 11th International Conference on Words (Montreal, September 11-15, 2017)